OpenStax University Physics/E&M/Alternating-Current Circuits

$ℰ & ℳ$ (Vol. 2): 5:Electric Charges and Fields 6:Gauss's Law 7:Electric Potential 8:Capacitance 9:Current and Resistance 10:Direct-Current Circuits 11:Magnetic Forces and Fields 12:Sources of Magnetic Fields 13:Electromagnetic Induction 14:Inductance 15:Alternating-Current Circuits 16:Electromagnetic Waves

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Chapter 15

Alternating-Current Circuits

AC voltage and current $v = V_{0} \sin (ω t - ϕ)$ if $i = I_{0} \sin ω t .$
▭ RMS values $I_{r m s} = \frac{I_{0}}{\sqrt{2}}$ and $V_{r m s} = \frac{V_{0}}{\sqrt{2}}$ ▭ Impedance $V_{0} = I_{0} X$

▭ Resistor $V_{0} = I_{0} X_{R}, ϕ = 0,$ where $X_{R} = R$
▭ Capacitor $V_{0} = I_{0} X_{C}, ϕ = - \frac{π}{2},$ where $X_{C} = \frac{1}{ω C}$ ▭ Inductor $V_{0} = I_{0} X_{L}, ϕ = + \frac{π}{2},$ where $X_{L} = ω L$
▭ RLC series circuit $V_{0} = I_{0} Z$ where $Z = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}$ and $ϕ = \tan^{- 1} \frac{X_{L} - X_{C}}{R}$
▭ Resonant angular frequency $ω_{0} = \sqrt{\frac{1}{L C}}$ ▭ Quality factor $Q = \frac{ω_{0}}{Δ ω} = \frac{ω_{0} L}{R}$
▭ Average power $P_{a v e} = \frac{1}{2} I_{0} V_{0} \cos ϕ = I_{r m s} V_{r m s} \cos ϕ$ , where $ϕ = 0$ for a resistor.
▭ Transformer voltages and currents $\frac{V_{S}}{V_{P}} = \frac{N_{S}}{N_{P}} = \frac{I_{P}}{I_{S}}$

For quiz at QB/d_cp2.15

AC voltage and current $v = V_{0} \sin (ω t - ϕ)$ if $i = I_{0} \sin ω t .$
RMS values $I_{r m s} = \frac{I_{0}}{\sqrt{2}}$ and $V_{r m s} = \frac{V_{0}}{\sqrt{2}}$
Impedance $V_{0} = I_{0} X$
Resistor $V_{0} = I_{0} X_{R}, ϕ = 0,$ where $X_{R} = R$
Capacitor $V_{0} = I_{0} X_{C}, ϕ = - \frac{π}{2},$ where $X_{C} = \frac{1}{ω C}$
Inductor $V_{0} = I_{0} X_{L}, ϕ = + \frac{π}{2},$ where $X_{L} = ω L$
RLC series circuit $V_{0} = I_{0} Z$ where $Z = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}$ and $ϕ = \tan^{- 1} \frac{X_{L} - X_{C}}{R}$
Resonant angular frequency $ω_{0} = \sqrt{\frac{1}{L C}}$
Quality factor $Q = \frac{ω_{0}}{Δ ω} = \frac{ω_{0} L}{R}$
Average power $P_{a v e} = \frac{1}{2} I_{0} V_{0} \cos ϕ = I_{r m s} V_{r m s} \cos ϕ$
Transformer voltages and currents $\frac{V_{S}}{V_{P}} = \frac{N_{S}}{N_{P}} = \frac{I_{P}}{I_{S}}$